This paper suggests an enhanced control scheme for a four-leg battery energy storage systems (BESS) under unbalanced and nonlinear load conditions operating in the isolated microgrid. Simplicity, tiny steady-state error, fast transient response, and low total harmonic distortion (THD) are the main advantages of the method. Firstly, a new decoupled per-phase model for the three-phase four-leg inverter is presented. It can eliminate the effect of power stage coupling on control design; thus, the three-phase four-leg power inverter can be viewed as three single input single output (SISO) control systems. Then, using an improved orthogonal signal generation method, the per-phase model of the four-leg inverter in the stationary and synchronous frame is derived. As the second step, a per-phase multi-loop control scheme for the four-leg inverter under unbalanced load conditions is suggested. The proposed control strategy has the ability to provide balanced output voltages under unbalanced load conditions by avoiding the need to deal with the symmetrical components. Finally, a multi-resonant harmonic compensator is used to actively prevent low-order harmonic currents to distort the output voltages of the three-phase four-leg grid-forming power converter. Simulations results are also presented to verify the performance of the suggested control strategy.
